The risk from an environmental contaminant is estimated with a risk equation involving the contaminant's concentration and other factors. Because the overall goal of risk management is to ensure such risks are not intolerably large, we need some way to back calculate from constraints on risk mandated by regulation or prudence to the allowable environmental concentration for the contaminant. It is now well known that the approach used in deterministic assessments of simply inverting the risk equation to compute the cleanup goal does not work in a probabilistic assessment. Several approaches have been proposed, but none is sufficiently general. We have developed simple and efficient methods to compute cleanup goals that satisfy multiple simultaneous criteria in the context of a probabilistic assessment. The approach can be used with multiple receptors and with arbitrarily many constraints on percentiles of the target risk. The proposed research will explore the properties of this approach, extend it to more complex problems involving multiple effects (e.g., the toxicant causes two diseases), multiple tropic levels (e.g., plankton to shellfish to humans), multiple exposure pathways (e.g., breathing, drinking, dermal absorption), multiple potentially synergistic toxicants, exposure advisories, and related areas of human health risk assessment. Case studies will be developed for each of these subject areas to demonstrate the workability of the approach and the results disseminated via the scientific literature. User-friendly software will be developed to make these methods available to risk management professionals.